to be published in: ASME Journal of Turbomachinery THE DESIGN OF AN IMPROVED ENDWALL FILM-COOLING CONFIGURATION

ASME Paper 98-GT-483 to be published in: ASME Journal of Turbomachinery THE DESIGN OF AN IMPROVED ENDWALL FILM-COOLING CONFIGURATION S. Friedrichs BMW Rolls-Royce GmbH Dahlewitz, Germany H.P. Hodson and W.N. Dawes Whittle Laboratory, University of Cambridge Cambridge, United Kingdom ABSTRACT The endwall film-cooling cooling configuration investigated by Friedrichs et al. (1996, 1997) had in principle sufficient cooling flow for the endwall, but in practice, the redistribution of this coolant by secondary flows left large endwall areas uncooled. This paper describes the attempt to improve upon this datum cooling configuration by redistributing the available coolant to provide a better coolant coverage on the endwall surface, whilst keeping the associated aerodynamic losses small. The design of the new, improved cooling configuration was based on the understanding of endwall film-cooling described by Friedrichs et al. (1996, 1997). Computational fluid dynamics were used to predict the basic flow and pressure field without coolant ejection. Using this as a basis, the above described understanding was used to place cooling holes so that they would provide the necessary cooling coverage at minimal aerodynamic penalty. The simple analytical modelling developed in Friedrichs et al. (1997) was then used to check that the coolant consumption and the increase in aerodynamic loss lay within the limits of the design goal. The improved cooling configuration was tested experimentally in a large scale, low speed linear cascade. An analysis of the results shows that the redesign of the cooling configuration has been successful in achieving an improved coolant coverage with lower aerodynamic losses, whilst using the same amount of coolant as in the datum cooling configuration. The improved cooling configuration has reconfirmed conclusions from Friedrichs et al. (1996, 1997); firstly, coolant ejection downstream of the three-dimensional separation lines on the endwall does not change the secondary flow structures; secondly, placement of holes in regions of high static pressure helps reduce the aerodynamic penalties of platform coolant ejection; finally, taking account of secondary flow can improve the design of endwall film-cooling configurations. NOMENCLATURE ρcoolant Vcoolant M = local blowing ratio ρfreestream Vfreestream inlet blowing ratio (blowing ratio of an idealised loss free coolant hole ejecting to inlet conditions) p inlet cascade inlet static pressure P 0 inlet cascade inlet stagnation pressure coolant plenum stagnation pressure P 0 plenum INTRODUCTION An increase in the thrust and cycle efficiency of gas turbines can be achieved through higher turbine entry temperatures. Maintaining adequate life at these temperatures requires the development of materials and efficient cooling methods. One cooling method that has gained increasing importance is endwall film-cooling, where coolant air is discharged through discrete holes in the inner and outer endwalls (platforms) of a turbine blade passage. After leaving the holes, the coolant forms a protective layer between the hot mainstream gas and the surface that is to be protected. The flow near the endwalls, into which the coolant is being ejected, is inherently three-dimensional due to the presence of secondary flow. The turning of the mainstream flow within the blade passage produces a blade-to-blade pressure gradient that generates a transverse component of flow within the endwall boundary layers. The inlet boundary layer undergoes three-dimensional separation and is entrained into vortices that are formed near the endwall. A general overview of secondary flow in turbine blade passages is given by Sieverding (1984). Harrison (1989) and Friedrichs et al. (1996, 1997) describe the secondary flow structures in the turbine cascade used in this investigation. The ejected coolant interacts with this three-dimensional flow. Friedrichs et al. (1996, 1997) found that this interaction not only influences the distribution of the coolant, and hence the cooling effectiveness, but also influences the generation of aerodynamic loss. They Presented at the International Gas Turbine & Aeroengine Congress and Exposition Stockholm, Sweden - June 2 - June 5, 1998 This paper has been accepted for publication in the Transactions of the ASME

concluded that it is necessary to take the three-dimensional nature of the endwall flow into account in the design of endwall film-cooling configurations. Coolant ejection locations have to be viewed with respect to the three-dimensional separation lines on the endwall, taking account of the fact that these can be changed due to upstream endwall coolant ejection. Previous investigations of endwall filmcooling, such as the ones by Blair (1974), Takeishi et al. (1989), Granser and Schulenberg (1990), Bourguignon (1985), Bario et al. (1989), Harasgama and Burton (1991), Jabbari et al. (1994), Goldman and McLallin (1977) and Sieverding and Wilputte (1980) support these conclusions. THE DATUM COOLING CONFIGURATION The datum cooling configuration as investigated by Friedrichs et al. (1996, 1997) could have provided a complete coolant coverage of the endwall in the absence of secondary flows. In practice, large uncooled areas remained (see Fig. 1). (1) (2) (4) basic understanding described by Friedrichs et al. (1996, 1997) and by using numerical modelling and prediction tools in the design process. The endwall film-cooling investigation presented here and in Friedrichs et al. (1996, 1997) was performed on a large-scale, low-speed, linear turbine cascade. The cascade consists of four blades with a true chord of 278 mm, a span of 300 mm, and a pitch of 230 mm. The flow enters the cascade at an angle of 40 and is turned through 105. With the low aspect ratio and high turning angle, the blades produce strong secondary flows. These are stronger than the ones found in high pressure turbine nozzle guide vanes with typical turning angles of 70 to 75, and therefore allow a more detailed observation of the basic interactions between endwall coolant ejection and the passage flow field. Details of the basic cascade without coolant ejection can be found in Harrison (1989). In both the datum and the improved cooling configuration, coolant air is ejected from a common plenum chamber through cylindrical holes in one endwall of the cascade. In both cooling configurations the holes have a diameter of 4 mm and eject at an angle of 30 to the surface. The thickness of the endwall is 12 mm, giving a length to diameter ratio of 6, typical of endwall film-cooling configurations. The datum cooling configuration is shown in Fig. 1. Rows of holes are located at four axial positions: upstream of the leading edge, at 30%, 60%, and 90% axial chord. Four single holes are located near the blade pressure surface. All of the holes, except for the row at 90% axial chord and the hole at the trailing edge, eject in approximately the inviscid streamline direction. This cooling configuration might be expected to provide cooling to most of the endwall surface in the absence of secondary flow effects. In practice, Fig. 1 shows that large uncooled areas remain. (3) Lift-Off Lines (1): Horseshoe Vortex (2): Pressure Side Leg of (1) (3): Suction Side Leg of (1) (4): Passage Vortex (4) 40% 30% Fig. 1: Adiabatic Film-Cooling Effectiveness on the Endwall Surface for the Datum Cooling Configuration, at an Inlet Blowing Ratio of = 1.0 (Friedrichs et al. 1996, 1997) Design Goal In this paper it will be attempted to improve upon the datum cooling configuration by redistributing coolant to provide a better coolant coverage on the endwall surface, whilst keeping the associated aerodynamic losses small. This goal is to be achieved by applying the Upstream of the Three-Dimensional Separation Lines The need for cooling upstream of the three-dimensional separation lines (lift-off lines) on the endwall is small. Inlet gas temperatures near the endwalls tend to be relatively cool as a result of combustor cooling and radial inlet temperature profiles. Heat transfer coefficients are also low in this region, due to low velocities and reasonably twodimensional flow. Upstream of the three-dimensional separation lines adequate coolant coverage at almost no aerodynamic penalty was already provided by the datum cooling configuration. If necessary, cooling performance could be increased by setting the holes in the row upstream of the leading edge at an angle to the local free stream to provide compound angle ejection. This will increase film-cooling effectiveness but will also increase aerodynamic losses due to enhanced mixing. Further improvements in cooling performance could be achieved by adding a second row of holes, staggered to the first one, or by using holes with flared exits (fan shaped holes). Downstream of the Three-Dimensional Separation Lines Downstream of the three-dimensional separation lines on the endwall there is a large need for cooling. Secondary flows, combined with radial inlet temperature profiles, result in hotter mainstream flow being swept down onto the endwall surfaces. Velocities are high and together with the new, thin boundary layer which is formed down- 2

stream of the three-dimensional separation lines this leads to elevated heat transfer coefficient levels. Providing the necessary coolant coverage downstream of the threedimensional separation lines has been shown to be more difficult, as there are interactions between the coolant ejected from the endwall and the secondary flow in the blade passage. The improved cooling configuration aims to provide cooling to all of the endwall surface in the blade passage downstream of the threedimensional separation lines. For this region, a uniform need for cooling is assumed. In practice there will be local variations in the need for cooling, which will have been determined by design experience and numerical predictions. As a result, there will be locally varying cooling design goals that can differ, even between hub and casing. The design goal for the improved cooling configuration was to achieve a complete coolant coverage downstream of the threedimensional separation lines at the same coolant consumption as that used by the holes of the datum cooling configuration located downstream of the three-dimensional separation lines. Furthermore, the aerodynamic penalty was to be less than or equal to that incurred by the downstream holes of the datum cooling configuration. DESIGNING THE IMPROVED COOLING CONFIGURATION The results from Friedrichs et al. (1996, 1997) have shown that in designing endwall film-cooling configurations it is necessary to take account of the interactions between the coolant ejected from the endwall and the secondary flow in the blade passage. This requires the interactions to be understood and it requires a prediction of the strengths and locations of the secondary flow structures. In addition, a prediction of the hole exit static pressure field is required. This will allow coolant consumption to be determined and can be used to estimate the loss increase due to coolant ejection by performing a mixing calculation such as the one described by Friedrichs et al. (1997). A structured mesh 3D Navier-Stokes prediction is able to give reasonable predictions of the flow and pressure fields in the blade passage without coolant ejection. Here, BTOB3D, a three-dimensional Navier-Stokes code written by Dawes (1988), was used for such a computational simulation. It solves the Reynolds averaged Navier- Stokes equations with a mixing length turbulence model on a structured grid H-Mesh. A time-marching procedure is used to advance the flow field from the initial guess to the converged solution. Local time stepping and multigrid acceleration are used to accelerate convergence to the steady-state. The simulation is not time accurate, but only uses the time stepping scheme to achieve a final steady-state solution. An adaptive artificial viscosity term is added to the governing equations to control odd-even point solution decoupling and to suppress oscillations in regions with strong pressure gradients. Details of the solution procedure and discretisation scheme are given by Dawes (1988). Computational simulations of the cascade without film-cooling were performed using two mesh resolutions, a medium one with ~125,000 nodes (33x115x33) and a fine one with ~670,000 nodes (93x153x47). The computational predictions were compared with measurements of the endwall static pressure field. The comparison showed good agreement for both the medium and the fine mesh resolutions, thus illustrating the expected mesh independence for these results. A comparison of computationally and experimentally determined stagnation pressure loss contours in the traversing plane located at 23% axial chord downstream of the trailing edges is shown in Fig. 2. As the flow in the computational prediction was compressible, an effective stagnation pressure loss was calculated from the entropy Midspan 23.0% 20.1% Endwall Medium Mesh 33x115x33 Fine Mesh 93x153x47 Experimental Result 22.1% Contour Interval: 0.03 Isentropic Exit Dynamic Pressure Dashed Lines Show Locations of Passage Vortex Core Centres Fig. 2: Comparison of Predicted and Measured Stagnation Pressure Loss Contours Without Coolant Ejection at 123% Axial Chord Fig. 3: Design of the Improved Cooling Configuration by Using an Uncooled 3D Navier-Stokes Prediction of the Endwall Surface-Flow to Estimate Coolant Trajectories 3

increase across the cascade. Although the depth of the wake and the loss core are overpredicted by the computational simulation, the comparison in Fig. 2 shows very good agreement of the shape and position of the loss core that is associated with the passage vortex, thus giving confidence in the correct prediction of the strengths and locations of the secondary flow structures. The endwall surface flow without coolant ejection, as predicted by using the medium mesh resolution, is visualised in Fig. 3 by tracing particle paths. The differences between the medium and fine mesh resolutions were small. In both cases the saddle point upstream of the leading edge, the three-dimensional separation lines on the endwall and the endwall crossflow can clearly be seen. Comparisons with the experimental surface-flow visualisation shown in Fig. 4, show that the location of the saddle point, the locations of the lift-off lines and the endwall crossflow are predicted reasonably well. Region 1 Region 1 Region 2 Region 3 (1) (2) Region 4 (3) (4) Lift-Off Lines (1): Horseshoe Vortex (2): Pressure Side Leg of (1) (3): Suction Side Leg of (1) (4): Passage Vortex Fig. 4: Oil and Dye Surface-Flow Visualisation on the Endwall Without Coolant Ejection (Friedrichs et al. (1996)) As illustrated in Fig. 3, a prediction of the surface-flow field without coolant ejection can be used to estimate coolant trajectories from potential ejection locations. The coolant trajectories shown in Fig. 3 were drawn by hand, superimposed on a printout of the predicted endwall surface-flow field. When estimating coolant trajectories in this way, account has to be taken of the fact that the surface-flow field can change under the influence of the ejected coolant (see Friedrichs et al. (1996, 1997)). For coolant ejection downstream of the threedimensional separation lines on the endwall, the investigations of Friedrichs et al. (1996, 1997) have shown that the strength of the endwall cross-flow is reduced, but the locations of the threedimensional separation lines remain unchanged. The endwall surface-flow, as visualised in Fig. 3, can be divided into several distinct regions requiring individual cooling hole placements. A schematic of the regions used for the design of the improved cooling configuration is shown in Fig. 5. Fig. 5: Schematic of the Regions of the Endwall Surface-Flow Requiring Individual Cooling Hole Placements (Only Downstream of the Three-Dimensional Separation Lines) The first region lies between the lift-off line of the leading edge horseshoe vortex and the leading edge itself. Cooling holes were placed around the leading edge in an attempt to use the endwall surface flow to provide coolant coverage for this region. The second region lies between the blade pressure surface and an imaginary line located halfway between the lift-off line of the main passage vortex and the blade pressure surface. The surface-flow in this region approximately follows the inviscid streamline direction, requiring a classical cooling hole arrangement. Two groups of holes with two staggered rows each are placed in this region to provide the necessary coolant coverage. The third region lies between the imaginary line described above and the lift-off line of the main passage vortex. This region experiences strong endwall cross-flow, with the surface-flow being turned from the inviscid streamline direction towards the blade suction surface. Several cooling holes are placed along the imaginary line that lies halfway between the lift-off line of the main passage vortex and the blade pressure surface. The strong endwall crossflow was expected to turn the ejected coolant towards the blade suction surface and so provide coolant coverage for this region. As there are no cooling holes upstream of this line, the endwall cross-flow was expected to remain unchanged under the influence of coolant ejection. The last region lies in the corner between the blade suction surface and the endwall. Two single holes are placed in this corner with the intention of feeding coolant into the corner vortex located here. The same BTOB3D calculation that was used to predict the endwall surface-flow shown in Fig. 3 was also used to predict the endwall static pressure field. This prediction was used to determine the exit 4

static pressures without coolant ejection for the holes of the improved cooling configuration. In the design phase of the improved cooling configuration, coolant consumption was estimated by using the predicted hole exit static pressures without coolant ejection together with a discharge coefficient that was estimated based on the datum cooling configuration. The individual hole mass flows obtained from this estimate were used in a constant static pressure mixing calculation (as described in Friedrichs et al. (1997)) to estimate the associated increase in aerodynamic loss. Both of these estimates were needed to determine whether the improved cooling configuration could be expected to meet the design goal with respect to coolant consumption and aerodynamic loss. The final design of the improved cooling configuration is shown in Fig. 6. The coolant holes are mostly placed in regions of high static pressure in an attempt to minimise the aerodynamic penalty of coolant ejection. Appropriate hole spacings were judged based on the experience gained with the datum cooling configuration (see Fig. 1). Possible manufacturing constraints in real engine applications were not taken into account. The estimated coolant coverage, coolant consumption and increase in aerodynamic loss promised to fulfil the design goal. Testing the improved coolant configuration confirmed the estimates; the results are given below. 60 90 60 90 90 90 90 90 0-20 -30 0-20 -30-30 -30-30 -30-30 -40-30 -30-30 -30-30 -40-50 -50-45 -60-60 Fig. 6: Cooling Hole Positions and Exit Angles of the Improved Cooling Configuration (Black Ellipses Indicate Hole Exit Locations on the Blade Passage Side of the Endwall) -65-68 TESTING THE IMPROVED COOLING CONFIGURATION The results presented in this paper and in Friedrichs et al. (1996, 1997) were produced with air being supplied to the common plenum chamber at approximately the same temperature as the free stream, resulting in a unity coolant to free stream density ratio. The cascade was operating at a Reynolds number of 8.6x10 5 based on exit velocity and true chord and an exit Mach number of 0.02. Harrison (1989) measured the inlet boundary layer at a point half an axial chord upstream of the leading edge and found it to have a thickness of 18 mm, a displacement thickness of 2.6 mm, a momentum thickness of 1.9 mm and a shape factor of 1.36. The inlet turbulence level of the free stream was 0.5%. The improved cooling configuration was tested at two different coolant supply pressures. As in Friedrichs et al. (1997), the coolant supply pressure can be characterised by defining an inlet blowing ratio. This is the blowing ratio that an idealised, loss free coolant hole would have when ejecting to inlet conditions. It is defined as: M inlet = P0 P plenum 0 inlet p p inlet inlet (Eq. 1) The inlet blowing ratio is different to the local blowing ratio M, which is defined individually for each hole as the coolant densityvelocity product divided by the freestream density-velocity product. Local blowing ratios M can be calculated from the total measured coolant massflow and the uncooled hole-exit static pressures, assuming a uniform discharge coefficient for all of the coolant holes. At an inlet blowing ratio of = 1.0, the coolant plenum pressure is equal to the inlet stagnation pressure. In this special case, all coolant holes operate with a local blowing ratio M 0.67, a value equal to the average discharge coefficient at = 1.0. Nonetheless, the individual hole mass flows vary with the endwall static pressure, increasing towards the cascade exit. For all other values of the local hole blowing ratios M will vary. Shown in Fig. 7 are the local blowing ratios determined for an inlet blowing ratio of = 2.0. The local blowing ratios can be seen to vary with the endwall static pressure between M = 0.87 near the passage exit and M near the stagnation point. This is important, as the tendency of coolant jets to lift-off the surface increases with local blowing ratio (lift-off is usually associated with a blowing ratio greater than unity). Coolant Consumption The coolant consumption of the improved cooling configuration was to be approximately equal to that of the holes located downstream of the three-dimensional separation lines in the datum cooling configuration. In the datum cooling configuration, these were the holes at 90% axial chord, at 60% axial chord, in the pressure surface and endwall corner and the four holes at 30% axial chord located next to the blade pressure surface. At = 1.0 (the design point) the coolant massflow through downstream holes of the datum cooling configuration was equal to 0.80% of the passage inlet massflow, if both endwalls had been cooled. At = 1.0 the coolant massflow through the improved cooling configuration was measured to be 0.79% of the passage inlet 5

massflow, if both endwalls had been cooled. Due to different flow characteristics these values differ at higher inlet blowing ratios, illustrating that not only the design point has to be analysed, but also deviations from this condition. At = 2.0, the downstream holes of the datum cooling configuration consumed 1.35% and the holes of the improved cooling configuration consumed 1.62% of the passage inlet massflow, if both endwalls had been cooled. of the blade passage can be expected to provide the intended coolant coverage. Downstream of ejection, coolant ejection reduces the endwall cross-flow and turns the endwall surface-flow towards the inviscid streamline direction. This was observed in the datum cooling configuration and can be observed in the region between the row of holes in the middle of the blade passage and the blade pressure surface (region 2). As the cooling design in this region assumes flow in approximately the inviscid streamline direction, the intended coolant coverage can be expected to be achieved. Uncooled Prediction of Endwall Static Pressure 0.300 0.100 0.200 0.600 0.700 0.400 0.500 0.800 (1) (2) (4) Lift-Off Lines (1): Horseshoe Vortex (2): Pressure Side Leg of (1) (3): Suction Side Leg of (1) (4): Passage Vortex 1.000 Local Blowing Ratios M local 0.91 1.75 1.63 1.200 5.3 1.70 1.80 1.68 1.79 1.64 1.60 1.40 1.19 1.10 1.06 1.05 1.05 0.97 1.03 0.92 0.88 0.88 0.87 1.100 (3) Fig. 8: Oil and Dye Surface-Flow Visualisation on the Film-Cooled Endwall at an Inlet Blowing Ratio of = 1.0 (1) (2) Lift-Off Lines (1): Horseshoe Vortex (2): Pressure Side Leg of (1) (3): Suction Side Leg of (1) (4): Passage Vortex Endwall Static Pressure Contours Expressed as (P0 inlet-p)/(p0 inlet-p exit ) 0.88 (4) Fig. 7: Endwall Static Pressure Contours Predicted Without Coolant Ejection and Local Hole Blowing Ratios for the Improved Cooling Configuration at = 2.0 (3) Surface-Flow Visualisation Fig. 8 and Fig. 9 show oil and dye visualisations of the endwall surface-flow under influence of coolant ejection. For ease of comparison, the lift-off lines determined from Fig. 8 and Fig. 9 are repeated in some of the following figures. A comparison with the uncooled surface-flow shown in Fig. 4 illustrates that the three-dimensional separation lines on the endwall are not affected by the downstream ejection. Similarly, the cross-flow in the region between the lift-off line of the main passage vortex and the row of holes in the middle of the blade passage (region 3) is not affected by coolant ejection. As a result, the row of holes in the middle Fig. 9: Oil and Dye Surface-Flow Visualisation on the Film-Cooled Endwall at an Inlet Blowing Ratio of Minlet = 2.0 Adiabatic Film-Cooling Effectiveness The improved cooling configuration was intended to provide complete coolant coverage for the endwall surface downstream of the 6

90 30% Fig. 10: Adiabatic Film-Cooling Effectiveness on the Endwall Surface for the Improved Cooling Configuration at = 1.0 Fig. 11: Adiabatic Film-Cooling Effectiveness on the Endwall Surface for the Improved Cooling Configuration at = 2.0 three-dimensional separation lines. To what extent this has been achieved can be seen in Fig. 10 and Fig. 11. These figures show the distributions of adiabatic film-cooling effectiveness on the endwall surface for inlet blowing ratios of = 1.0 and = 2.0, measured using the Ammonia and Diazo technique as described in Friedrichs et al. (1996). A comparison of the trailing edge regions of the upper and lower blades in Fig. 10 and Fig. 11 shows that only one passage was cooled. In order to reduce Ammonia consumption, only the holes visible in Fig. 10 and Fig. 11 were ejecting coolant; the rest of the holes shown in Fig. 6 were closed off. Fig. 10 and Fig. 11 show that providing coolant coverage around the blade leading edge is difficult, especially in the vicinity of the stagnation point. Hole exit static pressures are high, resulting in low coolant mass flows and high local blowing ratios. As Fig. 7 illustrates, local blowing ratios in the vicinity of the stagnation point rise disproportionately with inlet blowing ratio. As a result, coolant jets in this region are likely to have lifted off the surface at = 2.0. Hole exit static pressures fall around the suction side of the blade leading edge. As a result, the area between the lift-off line of the suction side leg of the leading edge horseshoe vortex and the blade is reasonably well cooled, even at the higher inlet blowing ratio of = 2.0. The two regions located between the lift-off line of the main passage vortex and the blade pressure surface are well cooled. Next to the blade pressure surface the two double rows of holes maintain a complete coolant coverage of above adiabatic film-cooling effectiveness. The coolant trajectories from the holes in the middle of the blade passage are turned towards the blade suction surface and provide an almost complete coolant coverage of above cooling effectiveness up to the lift-off line of the passage vortex. At the higher inlet blowing ratio the trajectories from the holes in the middle of the blade passage are not turned immediately, but follow the ejection direction in the vicinity of the holes. Nonetheless, they are eventually turned and with the help of the endwall cross-flow the coolant is distributed to provide the necessary coolant coverage. The blade suction surface and endwall corner is another region that is difficult to cool. Some cooling is provided from the two holes located in this region, but the levels of adiabatic film-cooling effectiveness are low and fall to under for = 1.0. The shape of the coolant trajectories from the two holes located in this region indicates the presence of a corner vortex, which is probably responsible for the difficulties in cooling this region. Axial variations of pitchwise averaged film-cooling effectiveness were determined for the improved configuration and the downstream holes of the datum cooling configuration, to enable quantitative comparisons to be made. Unfortunately such comparisons have to disregard any pitchwise variations in the cooling provided and the need for cooling. Similarly, an overall averaged value of film-cooling effectiveness can only be used for meaningful comparisons if a uniform need for cooling on the endwall is implicitly assumed. To take account of the local need for 7

Fig. 12: Schematic of the Endwall Regions Over Which the Averaging of Film-Cooling Effectiveness was Performed cooling, the endwall needs to be divided into regions which are defined by their local need for cooling. Averages for these regions can then be used for meaningful comparisons. Here the cooling performance of the improved cooling configuration is compared to that of the datum cooling configuration. The region used for comparison is shown in Fig. 12; it is the endwall surface downstream of the three-dimensional separation lines, between the leading and trailing edge planes. When the pitchwise averages were performed for this region, the hole and blade cut-outs and the endwall surface upstream of the three-dimensional separation lines were disregarded in the averaging process. Comparisons of the axial variations of pitchwise averaged filmcooling effectiveness for the improved configuration and the downstream holes of the datum cooling configuration are shown in Fig. 13 and Fig. 14. These axial variations were used to determine an overall average film-cooling effectiveness for the endwall surface downstream of the three-dimensional separation lines, between the leading and trailing edge planes. The axial variations of the pitchwise averages reflect the fact that the improved cooling configuration no longer has the large, uncooled areas observed in the datum cooling configuration. The basic tendency remains; the pitchwise averaged film-cooling effectiveness rises towards the rear of the blade passage. At = 1.0 the improved cooling configuration provides a significantly higher average cooling effectiveness (19.40%) than the downstream holes of the datum cooling configuration (12.75%). At = 2.0 the difference between the two is smaller, but still the improved cooling configuration provides a higher average film-cooling effectiveness (16.61% vs. 14.30%). The average cooling effectiveness of the datum cooling configuration increases with increasing inlet blowing ratio, whereas the improved cooling configuration displays a reduced average cooling effectiveness at the higher inlet blowing ra- Effectiveness [%] 50. 40. 30. Leading Edge Downstream Holes of the Datum Cooling Configuration Trailing Edge Effectiveness [%] 50. 40. 30. Leading Edge Downstream Holes of the Datum Cooling Configuration Trailing Edge 20. Average: 12.75% 20. Average: 14.30% 10. 10. 0. -20. 0. 20. 40. 60. 80. 100. 120. 140. Axial Distance / Axial Chord [%] 0. -20. 0. 20. 40. 60. 80. 100. 120. 140. Axial Distance / Axial Chord [%] Effectiveness [%] 50. 40. 30. Leading Edge Improved Cooling Configuration Trailing Edge Effectiveness [%] 50. 40. 30. Leading Edge Improved Cooling Configuration Trailing Edge 20. Average: 19.40% 20. Average: 16.61% 10. 10. 0. -20. 0. 20. 40. 60. 80. 100. 120. 140. Axial Distance / Axial Chord [%] Fig. 13: Axial Variation of Pitchwise Averaged Film-Cooling Effectiveness for the Improved Cooling Configuration and the Downstream Holes of the Datum Configuration at = 1.0 0. -20. 0. 20. 40. 60. 80. 100. 120. 140. Axial Distance / Axial Chord [%] Fig. 14: Axial Variation of Pitchwise Averaged Film-Cooling Effectiveness for the Improved Cooling Configuration and the Downstream Holes of the Datum Configuration at = 2.0 8

tio. The axial variations of pitchwise averages show that this is due to a reduced effectiveness of the holes in the first half of the blade passage, as a result of the coolant having the tendency to lift off the surface. To quantify cooling performance, the achieved levels of average film-cooling effectiveness have to be compared to the amount of coolant used. This has been done by dividing the cooling effectiveness by the coolant mass flow, expressed as percentage of the passage mass flow if both endwalls had been cooled, and is shown in Tab. 1. Effectiveness per % Coolant Flow Datum Configuration Downstream Holes Improved Cooling Configuration = 1.0 15.9% 24.6% = 2.0 10.6% 10.3% Tab. 1: Comparison of the Average Film-Cooling Effectiveness, per Percent Coolant Mass Flow, of the Improved Cooling Configuration and the Downstream Holes of the Datum Configuration A comparison of the values shown in Tab. 1 clearly shows the increased cooling performance of the improved cooling configuration. At the design condition of = 1.0, the improved cooling configuration displays a cooling performance that is over 50% higher than the downstream holes of the datum cooling configuration. At the higher inlet blowing ratio of 2.0, the cooling performances of the two cooling configurations are similar. Both cooling configurations are more efficient at the lower inlet blowing ratio. The assessment of cooling performance given above was made under the assumption that the heat transfer coefficient distribution hardly changes between the two cooling configurations. Strictly speaking, one should compare heat flux levels, as they are responsible for the resulting metal temperatures. Nonetheless, adiabatic film-cooling effectiveness describes the distribution of the coolant and is considered to be the dominating parameter. Aerodynamic Performance The flow field downstream of the cascade was measured in an axial plane located at 23% axial chord downstream of the trailing edges. Measurements were performed with and without coolant ejection from the improved cooling configuration. The traversing plane for these aerodynamic measurements is the same as for the datum cooling configuration (see Friedrichs et al. (1997)). It is shifted relative to the wake centrelines to capture the entire wake and loss core downstream of a blade. As this traversing plane covers fluid from two neighbouring passages, both of these passages were cooled as shown in Fig. 6. Fig. 15 shows contours of stagnation pressure loss with and without coolant ejection. The uncooled measurements from Friedrichs et al. (1997) (shown in Fig. 2) were repeated to obtain a new datum, after the cascade was dismantled to install a new endwall with the improved cooling configuration. The uncooled contour plot in Fig. 15 shows only subtle differences to the uncooled contour plot in Fig. 2. The very small differences between the two illustrate excellent repeatability, even after a reassembly of the experimental setup. A comparison of the loss contours and the spanwise positions of the passage vortex core centres with and without coolant ejection shows that coolant ejection from the improved cooling configuration Midspan 22.0% Endwall 22.7% Uncooled = 1.0 = 2.0 has almost no effect on the secondary flow downstream of the cascade. As expected, the biggest differences can be observed in the endwall exit boundary layer which is slightly thickened due to coolant ejection. Tab. 2 shows a comparison of the loss increase, per percent coolant flow, of the 'downstream' holes of the datum cooling configuration and the improved cooling configuration. The improved cooling configuration displays lower loss increases, per percent coolant flow, at both inlet blowing ratios. The absolute loss increases, even at the higher coolant consumption of the improved cooling configuration at = 2.0, are lower than for the downstream holes of the datum cooling configuration. Loss Increase per % Coolant Flow Datum Configuration Downstream Holes Improved Cooling Configuration = 1.0 0.68% 0.44% = 2.0 0.81% 0.66% Tab. 2: Comparison of the Loss Increase, per Percent Coolant Mass Flow, of the 'Downstream' Holes of the Datum Cooling Configuration and the Improved Cooling Configuration Fig. 16 shows a comparison of the measured and predicted loss increases, per percent coolant flow, for the improved cooling configuration and the downstream holes of the datum cooling configuration. The predictions were performed by using the measured coolant mass flow, the predicted hole exit static pressures and a constant static pressure mixing calculation as described in Friedrichs et al. (1997). The measured loss increases are consistently lower than the sum of the hole and mixing losses, indicating some form of loss reduction in the blade passage. As the secondary flow structures were shown to be unchanged due to coolant ejection downstream of the threedimensional separation lines, it has to be assumed that the difference is due to reduced loss production on the endwall surfaces and measurement and modelling uncertainties. (Uncertainty for the experimentally determined mixed-out loss coefficient is ±0.12% of the isentropic exit dynamic pressure.) Nonetheless, the predicted loss increases display the same trend as the measured loss increases; both indicate that the improved cooling configuration incurs less aerodynamic penalty than the downstream holes of the datum cooling configuration, thus fulfilling the aerodynamic part of the design goal. 22.8% 0.06 0.06 0.06 0.03 0.03 0.03 Contour Interval: 0.03 Isentropic Exit Dynamic Pressure Dashed Lines Show Locations of Passage Vortex Core Centres Fig. 15: Contours of Stagnation Pressure Loss for All of the Holes of the Improved Cooling Configuration Blowing Simultaneously 9

Loss Increase Per % Coolant Flow 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00 Downstream Holes Datum Configuration Measured Mixing (Predicted) Hole (Predicted) Improved Configuration 1.0 2.0 1.0 2.0 Fig. 16: Comparison of Measured and Calculated Losses, per Percent Coolant Massflow, for the Two Cooling Configurations READ-ACROSS TO ENGINE DESIGN The investigations described in this paper were performed in a low speed, linear cascade. This is a simplified model of high pressure turbine nozzle guide vanes in real engines. Many effects, such as inlet pressure and temperature profiles, inlet turbulence levels, radial pressure gradients, gaps and steps in the endwalls between neighbouring vanes, transonic flow, endwall hot spots and coolant to mainstream density ratios are not modelled in the experiments. These effects will have their impact on the secondary flow structures, the endwall boundary layers and the behaviour of the coolant jets. Therefore, it is not the cooling design from Fig. 6 that should be transferred to the engine environment, but rather the basic design methodology presented in this paper. Comparisons with engine geometries, or with other cooling configurations, should be performed relative to the secondary flow structures and the endwall surface flow. Comparisons with other operating conditions should be performed on the basis of momentum ratios. Analogous to the definition of the inlet blowing ratio (Eq. 1), an inlet momentum ratio I inlet can be defined to characterise the coolant supply pressure. This would then be the momentum ratio that an idealised loss free coolant hole would have when ejecting to inlet conditions. An example: For a gas turbine with an inlet mach number of 0.15, a ratio of plenum to inlet stagnation pressure of 1.03, a ratio of specific heat capacities for the coolant of 1.36 and a ratio of specific heat capacities for the mainstream of 1.28, the inlet momentum ratio I inlet is equal to 3.07. The corresponding experiments in this paper (with unity density ratio) would have had an inlet blowing ratio of 1.75. For this hypothetical engine case, the design point would be at a higher inlet blowing (momentum) ratio and would perhaps require a cooling design which is more resistant to coolant jet lift-off in regions of high exit static pressure (for example through compound angle ejection or holes with shaped exits). The basic design methodology, however, would be the one presented in this paper, i.e. using an uncooled CFD prediction of the actual secondary flows, dividing the endwalls into regions and then providing coolant to these regions dependent on the local need for cooling. CONCLUSIONS The redesign of the cooling configuration downstream of the threedimensional separation lines on the endwall has been successful in achieving improved coolant coverage with lower aerodynamic losses, whilst using the same amount of coolant as in the datum cooling configuration. The maximum benefits are achieved at the design point of = 1.0. At the higher inlet blowing ratio of = 2.0, the redesign has a coolant consumption that is higher than in the datum configuration. However, the aerodynamic penalty is reduced and an improved coolant coverage is obtained. The design of the improved cooling configuration was based on the understanding and the numerical modelling described by Friedrichs et al. (1996, 1997). Computational fluid dynamics were used to predict the basic flow field and pressure field in the cascade without coolant ejection. Using this as a basis, the previously gained understanding was used to place cooling holes so that they would provide the necessary cooling coverage at minimal aerodynamic penalty. Simple analytical modelling was then used to check that the coolant consumption and the increase in aerodynamic loss lay within the limits of the design goal. The improved cooling configuration exhibited interactions between the secondary flow and the ejected coolant similar to those observed by Friedrichs et al. (1996, 1997). It can be concluded, that firstly, coolant ejection downstream of the three-dimensional separation lines on the endwall does not change the secondary flow structures. Secondly, placement of holes in regions of high static pressure helps to reduce the aerodynamic penalties of platform coolant ejection. Finally, taking account of the secondary flow and the interactions between the ejected coolant and the secondary flow can improve the design of endwall film-cooling configurations. ACKNOWLEDGEMENTS The authors are grateful for the support provided by Rolls-Royce plc, the Engineering & Physical Sciences Research Council (EPSRC), the Frankfurt Main Flughafen Stiftung (Frankfurt Main Airport Foundation) and BMW Rolls-Royce GmbH. They would also like to thank Prof. Denton for the use of the cascade and the technical staff of the Whittle Laboratory for their assistance. REFERENCES Bario, F., Leboeuf, F., Onvani, A., and Seddini, A., 1989, Aerodynamics of Cooling Jets Introduced in the Secondary Flow of a Low Speed Turbine Cascade, ASME Paper 89-GT-192 Blair, M.F., 1974, An Experimental Study of Heat Transfer and Film Cooling on Large-Scale Turbine Endwalls, ASME Journal of Heat Transfer, Vol. 96, pp. 524-529 Bourguignon, A.E., 1985, Etudes des Transferts Thermiques sur les Plates-Formes de Distributeur de Turbine avec et sans Film de Refroidissement, AGARD-CP-390, Heat Transfer and Cooling in Gas Turbines Dawes, W.N., 1988, "A Computer Program for the Analysis of Three Dimensional Viscous Compressible Flow in Turbomachinery Blade Rows", Whittle Laboratory, University of Cambridge 10

Friedrichs, S., Hodson, H.P., and Dawes, W.N., 1996, Distribution of Film-Cooling Effectiveness on a Turbine Endwall Measured Using the Ammonia and Diazo Technique, ASME Journal of Turbomachinery, Vol. 118, pp. 613-621 Friedrichs, S., Hodson, H.P. and Dawes, W.N., 1997, Aerodynamic Aspects of Endwall Film-Cooling, ASME Journal of Turbomachinery, Vol. 119, pp. 786-793 Goldman, L.J. and McLallin, K.L., 1977, Effect of Endwall Cooling on Secondary Flows in Turbine Stator Vanes, AGARD- CPP-214 Granser, D. and Schulenberg, T., 1990, Prediction and Measurement of Film Cooling Effectiveness for a First-Stage Turbine Vane Shroud, ASME Paper 90-GT-95 Harasgama, S.P. and Burton, C.D., 1991, Film Cooling Research on the Endwall of a Turbine Nozzle Guide Vane in a Short Duration Annular Cascade, Part 1: Experimental Technique and Results, ASME Paper 91-GT-252 Harrison, S., 1989, The Influence of Blade Stacking on Turbine Losses, Ph.D. Thesis, University of Cambridge; see also Harrison, S., 1989, Secondary Loss Generation in a Linear Cascade of High- Turning Turbine Blades, ASME Paper 89-GT-47 Jabbari, M.Y., Marston, K.C., Eckert, E.R.G., and Goldstein, R.J., 1994, Film Cooling of the Gas Turbine Endwall by Discrete-Hole Injection, ASME Paper 94-GT-67 Sieverding, C.H., 1984, Recent Progress in the Understanding of Basic Aspects of Secondary Flows in Turbine Blade Passages, ASME Journal of Engineering for Gas Turbines and Power, Vol. 107, pp. 248-257 Sieverding, C.H. and Wilputte, P., 1980, Influence of Mach Number and Endwall Cooling on Secondary Flows in a Straight Nozzle Cascade, ASME Paper 80-GT-52 Takeishi, K., Matsuura, M., Aoki, S., and Sato, T., 1989, An Experimental Study of Heat Transfer and Film Cooling on Low Aspect Ratio Turbine Nozzles, ASME Paper 89-GT-187 11